Finding the Day of the Week

Mental Math · Axiom Academy

Learn a systematic method to mentally calculate the day of the week for any date in history The Doomsday Algorithm was invented by mathematician John Conway. The key insight is that certain dates always fall on the same day of the week within any given year. We call this day the "Doomsday" for that year. Every century has an anchor day - the Doomsday for years ending in 00. This is our starting point for any calculation. The pattern repeats every 400 years: Tuesday → Sunday → Friday → Wednesday 3. Calculating the Year's Doomsday Now we adjust from the century anchor to find the Doomsday for our specific year using a simple formula. For a year YY (the last 2 digits): Divide by 4 (ignore remainder): YY ÷ 4 Add these together: YY + (YY ÷ 4) Add the century anchor day number Take the result mod 7 to get the day of the week Days: Sunday=0, Monday=1, Tuesday=2, Wednesday=3, Thursday=4, Friday=5, Saturday=6 Once you know the Doomsday for your year, you can find any date by counting days from a nearby Doomsday anchor. The last day of February (28th or 29th in leap years) March 0 (same as last day of February) 4/4, 6/6, 8/8, 10/10, 12/12 (even months) 5/9, 9/5, 7/11, 11/7 (odd months - "9 to 5 at 7-11") January: 3rd (or 4th in leap years) Nearest anchor: 7/11 is a Thursday Count back 7 days: July 4 is also a Thursday! Let's work through a complete example from start to finish: What day of the week was December 25, 1995? Century Anchor: 1900s → Wednesday (day 3)

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